Name
Abstract | ||
|---|---|---|
In rotor-router aggregation on the square lattice Z(2), particles starting at the origin perform deterministic analogues of random walks until reaching an unoccupied site. The limiting shape of the cluster of occupied sites is a disk. We consider a small change to the routing mechanism for sites on the x- and y-axes, resulting in a limiting shape which is a diamond instead of a disk. We show that for a certain choice of initial rotors, the occupied cluster grows as a perfect diamond. |
Year | Venue | Keywords |
|---|---|---|
2010 | ELECTRONIC JOURNAL OF COMBINATORICS | strong abelian property. the second author was partly supported by a national science foundation postdoctoral fellowship.,rotor-router aggregation,growth model,. asymptotic shape,low discrepancy,random walk |
Field | DocType | Volume |
Diamond,Combinatorics,Square lattice,Random walk,Rotor (electric),Router,Geometry,Mathematics,Limiting | Journal | 17.0 |
Issue | ISSN | Citations |
1.0 | 1077-8926 | 3 |
PageRank | References | Authors |
0.57 | 5 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Wouter Kager | 1 | 3 | 0.91 |
| Lionel Levine | 2 | 31 | 5.43 |